Theoretical 3D electron diffraction electrostatic potential maps of proteins modeled with a multipolar pseudoatom data bank

Accurate electrostatic potential maps and electron-density maps of proteins are calculated based on the transferable aspherical atom model using a pseudoatom data bank and are compared with the experimental data.


S1 Generation of reflection indices for lysozyme
In a typical diffraction experiment, the reflection intensities and their indices are collected. In order to calculate the theoretical structure factors for a given crystal, the indices of the reflections in the reciprocal space up to a given resolution are essential. Here, we calculate the reflection indices that correspond to the lysozyme crystal structure PDB ID 5k7o with the experimental unit cell parameters a = 76.232, b = 76.232, c = 37.141, α = β = γ = 90.00 and space group P 4 3 2 1 2. The reported resolution for this structure was 1.8Å. Since the indices depend also on the space group and are redundant, it is not necessary to calculate them for the full Ewald sphere. The reflection file is generated in sortav.hkl format and assigns the same intensity for all reflections (the intensity value is not used further by our programs). The systematic absences are not taken into account for simplicity.

S2 Recalculation of the electrostatic potential density
The electrostatic potential density maps are initially calculated by our programs

S3 Completeness
Fig. S1. Electrostatic potential density maps calculated using the electron scattering factors and based on the Transferable Aspherical Atom Model (eTAAM) of the (a) lysozyme structure at 1.8Å, (b) proteinase K structure at 1.75Å resolution.The experimental structures factor indices were deposited for both datasets with 96.83% and 94.12% completeness, respectively. The reflections indices from those datasets were taken to calculate the structure factors for the theoretical TAAM maps presented here in red. The maps shown in pink were generated based on the structure factors with reflection indices with 100% completeness. The maps are encompassing the region 15Å from the atom CD2 and CG, respectively. The voxel values of all calculated maps are scaled to the standard deviation equal to 1 and the average value of 0, their 2 sigma contours are shown. The maps take into account the thermal smearing effects.

S4 The covalent radius averaging method
Here, we present a simple method to compare the experimental and theoretical density maps in a quantitative manner close to atom positions. This method is more accurate than sampling the density values at atom positions. The averaging of voxel values over the grids sampled within the covalent radius distance from atom positions is performed. Schematic justification for using the covalent radius averaging method is shown in Figure S2. Since the voxels in the experimental map are large, the assessment of the density map at the atom position only, marked with a black cross, depends mostly on the position of the voxels with respect to the atomic structure. By sampling the density map within the covalent radius distance for each atom (here 0.6Å for oxygen), many sampled grid points make the assessment more accurate. The sampling radius is different for each element and it results in a different number of the sampled grid points, as shown in Table S1. The encompassed density is sampled every 0.1Å within the covalent radius of each atom. Calculated density maps are calculated using 0.3Å voxels.

S6 Map and rank correlation coefficients
Map correlation coefficient about mean (CC) and rank correlation coefficient (CC r ) between two density maps of lysozyme and proteinase K are presented in Tables S2 and S3. The calculation is done in two ways: for a full density map (a cube containing one protein molecule with solvent) and a protein fragment (a 10Å cube centered on the chosen atom buried inside the protein, almost no solvent). In the case of lysozyme, the 10Å cube was centered on the CA atom of Ile 55 residue, whereas in the proteinase K, the Ala 231 residue was chosen. Exp stands for the experimental density map, eTAAM and eIAM are the calculated electrostatic potential density maps with or without B-factors, scaled to match the standard deviation and the average value of the experimental map.

S9 R factor analysis
In order to quantify the impact of the TAAM/IAM, thermal smearing and the electron/X-ray scattering factors on the structure factors, we have calculated the R factors, presented in Table S5. The point of this analysis was to order the impact of the latter variants of the calculations. The difference between eTAAM with B and eIAM with B, which is equal to 13%, can be contrasted with the value of R factor (Observed) reported by the authors of the original eIAM refinement: 24.16%. Note that all the R factor values mentioned in Table S5 come from calculations between pairs of models being at absolute scale, not from the refinement procedure. The R factors calculated between the eTAAM and eIAM structure factors are higher than those for xTAAM and xIAM, which underlines the fact that for electron diffraction the choice of the model plays a more significant role than for X-ray diffraction. Nevertheless, all the values are lower than 13% so the choice of the model does not apply huge changes to the structure factors. Upon applying thermal smearing, the structure factors show larger deviation, while the largest impact on the structure factors comes from switching between electron and X-ray scattering factors.